Problems and Solutions in Mathematical Finance
Equity Derivatives, Volume 2
Wiley Finance Series (Band Nr. 2)
1. Auflage Februar 2017
856 Seiten, Hardcover
Wiley & Sons Ltd
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An essential reference for practitioners and students of quantitative finance
Financial analysts and investment bankers utilize mathematical finance tenets constantly in their encounters with financial markets, making a firm grasp of quantitative skills essential to a successful practitioner. Building upon the stochastic calculus basis established in Volume I, Problems and Solutions in Mathematical Finance Volume II concentrates on the study of equity, currency, and commodity derivatives. In their sequel study on mathematical finance, quantitative analysts Dr. Eric Chin and Dian Nel and risk management professor Dr. Sverrir Olafsson provide examples of both basic derivative securities and advanced model parameters. Mathematical and computational finance rely on computational intelligence, numerical methods, and computer simulations to make trading, hedging, and investment decisions, to determine the risk of those decisions, and to define price derivatives.
* Details the problem-solving process that determines popular option pricing techniques including procedures from closed-form solutions to numerical methods
* Provides the background required to enrich a career based in equities, currency, and commodity derivatives
For students and practitioners of quantitative finance, the detailed explanations of equity derivatives in this book will enrich any study of financial markets.
About the Authors xi
1 Basic Equity Derivatives Theory 1
1.1 Introduction 1
1.2 Problems and Solutions 8
1.2.1 Forward and Futures Contracts 8
1.2.2 Options Theory 15
1.2.3 Hedging Strategies 27
2 European Options 63
2.1 Introduction 63
2.2 Problems and Solutions 74
2.2.1 Basic Properties 74
2.2.2 Black-Scholes Model 89
2.2.3 Tree-Based Methods 190
2.2.4 The Greeks 218
3 American Options 267
3.1 Introduction 267
3.2 Problems and Solutions 271
3.2.1 Basic Properties 271
3.2.2 Time-Independent Options 292
3.2.3 Time-Dependent Options 305
4 Barrier Options 351
4.1 Introduction 351
4.2 Problems and Solutions 357
4.2.1 Probabilistic Approach 357
4.2.2 Reflection Principle Approach 386
4.2.3 Further Barrier-Style Options 408
5 Asian Options 439
5.1 Introduction 439
5.2 Problems and Solutions 443
5.2.1 Discrete Sampling 443
5.2.2 Continuous Sampling 480
6 Exotic Options 531
6.1 Introduction 531
6.2 Problems and Solutions 532
6.2.1 Path-Independent Options 532
6.2.2 Path-Dependent Options 586
7 Volatility Models 647
7.1 Introduction 647
7.2 Problems and Solutions 652
7.2.1 Historical and Implied Volatility 652
7.2.2 Local Volatility 685
7.2.3 Stochastic Volatility 710
7.2.4 Volatility Derivatives 769
A Mathematics Formulae 787
B Probability Theory Formulae 797
C Differential Equations Formulae 813
Bibliography 821
Notation 825
Index 829
